Pat the cod very dry. Use paper towels to remove as much surface moisture as possible. This helps the fish sear and keeps it from steaming.
Season simply. Sprinkle both sides with salt, pepper, and paprika. Let it sit at room temperature for 10 minutes while you prep the garlic and lemon.
Preheat the pan. Set a large nonstick or well-seasoned skillet over medium-high heat.
Add the olive oil and let it shimmer.
Sear the fish. Place the cod in the pan and cook undisturbed for 2 to 3 minutes until the bottom turns opaque and lightly golden. Carefully flip and cook another 2 to 3 minutes, depending on thickness, until the fish is nearly cooked through and flakes easily.
Lower heat and make the sauce. Reduce heat to medium-low. Push the fish to one side of the pan.
Add the butter to the empty side. When it melts, add the garlic and cook 30 to 45 seconds until fragrant, not browned.
Brighten it up. Stir in lemon zest, lemon juice, and broth (if using). Swirl the pan so the sauce mingles with the cod.
Spoon the garlicky butter over the fish for 30 to 60 seconds.
Finish with herbs and heat. Sprinkle parsley and red pepper flakes over the top. Taste the sauce and adjust salt and lemon as needed.
Serve right away. Plate the cod, spoon the sauce over, and add lemon wedges on the side.